How to create iridescent glossy tile material?
I was able to achieve something heading toward what you were describing anyway. I'm sure that there can be a lot of polish applied to this answer, especially on the cycle material nodes, but I believe that this will suffice to show the initial intent.

Here's the cycles material:



Here's the demo of the setup:



The geometry is two parts:


The first part is the tile itself, set to a basic glass material.
Inside the tile is a highly subdivided plane with two copies of a displacement modifier, to break up the normal directions within the tile. 


The cycles material does the rest of the heavy lifting.

Here's the blend for your reference: